Finite volume schemes for multi-dimensional hyperbolic systems based on the use of bicharacteristics

Mária Lukáčová-Medviďová; Jitka Saibertová

Applications of Mathematics (2006)

  • Volume: 51, Issue: 3, page 205-228
  • ISSN: 0862-7940

Abstract

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In this paper we present recent results for the bicharacteristic based finite volume schemes, the so-called finite volume evolution Galerkin (FVEG) schemes. These methods were proposed to solve multi-dimensional hyperbolic conservation laws. They combine the usually conflicting design objectives of using the conservation form and following the characteristics, or bicharacteristics. This is realized by combining the finite volume formulation with approximate evolution operators, which use bicharacteristics of the multi-dimensional hyperbolic system. In this way all of the infinitely many directions of wave propagation are taken into account. The main goal of this paper is to present a self-contained overview on the recent results. We study the L 1 -stability of the finite volume schemes obtained by various approximations of the flux integrals. Several numerical experiments presented in the last section confirm robustness and correct multi-dimensional behaviour of the FVEG methods.

How to cite

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Lukáčová-Medviďová, Mária, and Saibertová, Jitka. "Finite volume schemes for multi-dimensional hyperbolic systems based on the use of bicharacteristics." Applications of Mathematics 51.3 (2006): 205-228. <http://eudml.org/doc/33251>.

@article{Lukáčová2006,
abstract = {In this paper we present recent results for the bicharacteristic based finite volume schemes, the so-called finite volume evolution Galerkin (FVEG) schemes. These methods were proposed to solve multi-dimensional hyperbolic conservation laws. They combine the usually conflicting design objectives of using the conservation form and following the characteristics, or bicharacteristics. This is realized by combining the finite volume formulation with approximate evolution operators, which use bicharacteristics of the multi-dimensional hyperbolic system. In this way all of the infinitely many directions of wave propagation are taken into account. The main goal of this paper is to present a self-contained overview on the recent results. We study the $L^1$-stability of the finite volume schemes obtained by various approximations of the flux integrals. Several numerical experiments presented in the last section confirm robustness and correct multi-dimensional behaviour of the FVEG methods.},
author = {Lukáčová-Medviďová, Mária, Saibertová, Jitka},
journal = {Applications of Mathematics},
keywords = {multidimensional finite volume methods; bicharacteristics; hyperbolic systems; wave equation; Euler equations; multidimensional finite volume methods; bicharacteristics; hyperbolic systems; wave equation; Euler equations},
language = {eng},
number = {3},
pages = {205-228},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Finite volume schemes for multi-dimensional hyperbolic systems based on the use of bicharacteristics},
url = {http://eudml.org/doc/33251},
volume = {51},
year = {2006},
}

TY - JOUR
AU - Lukáčová-Medviďová, Mária
AU - Saibertová, Jitka
TI - Finite volume schemes for multi-dimensional hyperbolic systems based on the use of bicharacteristics
JO - Applications of Mathematics
PY - 2006
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 51
IS - 3
SP - 205
EP - 228
AB - In this paper we present recent results for the bicharacteristic based finite volume schemes, the so-called finite volume evolution Galerkin (FVEG) schemes. These methods were proposed to solve multi-dimensional hyperbolic conservation laws. They combine the usually conflicting design objectives of using the conservation form and following the characteristics, or bicharacteristics. This is realized by combining the finite volume formulation with approximate evolution operators, which use bicharacteristics of the multi-dimensional hyperbolic system. In this way all of the infinitely many directions of wave propagation are taken into account. The main goal of this paper is to present a self-contained overview on the recent results. We study the $L^1$-stability of the finite volume schemes obtained by various approximations of the flux integrals. Several numerical experiments presented in the last section confirm robustness and correct multi-dimensional behaviour of the FVEG methods.
LA - eng
KW - multidimensional finite volume methods; bicharacteristics; hyperbolic systems; wave equation; Euler equations; multidimensional finite volume methods; bicharacteristics; hyperbolic systems; wave equation; Euler equations
UR - http://eudml.org/doc/33251
ER -

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